Hey Shaily,
I understand you want to know if the same relations hold when going from frequency to time in the inverse Fourier transform as going from time to frequency domain . You also want to know if there is more efficient method to obtain the time domain representation for a function with a large frequency difference, without requiring a high number of points in the numerical calculation.
The same relations hold true means if you have a frequency range "f = (0:N-1)*deltaf", then the corresponding time range can be obtained as "t = (0:N-1)ts", where "ts = 1/(Ndeltaf)".
In your case, with a frequency range spanning from 4E9 Hz to 4.5E9 Hz (500 MHz), there is a large frequency difference between 0 and your given range. To efficiently obtain the time domain representation without requiring a large number of points, you have a few options:
- Shifting the function in the frequency domain: By centering the function at zero frequency, you can reduce the range of frequencies to consider. However, this approach introduces a missing phase in the inverse Fourier transform function in the time domain.
- Zero-padding: Another approach is to use zero-padding techniques. By adding zeros to your frequency domain data, you can increase the number of points and achieve a finer time resolution without losing accuracy. Zero-padding does not add additional information, but it allows you to capture a wider frequency range efficiently.
By considering these strategies, you can obtain the time domain from the frequency domain when calculating the numerical inverse Fourier transform while balancing efficiency and accuracy.
Hope this helps!
Regards,
Ayush Goyal
